Space variability impacts on hydrological responses of nature-based solutions and the resulting uncertainty: a case study of Guyancourt (France)

During the last few decades, the urban hydrological cycle has been strongly modified by the built environment, resulting in fast runoff and increasing the risk of waterlogging. Nature-based solutions (NBSs), which apply green infrastructures, have been more and more widely considered as a sustainable approach for urban storm water management. However, the assessment of NBS performance still requires further modelling development because of hydrological modelling results strongly depend on the representation of the multiscale space variability of both the rainfall and the NBS distributions. Indeed, we initially argue this issue with the help of the multifractal intersection theorem. To illustrate the importance of this question, the spatial heterogeneous distributions of two series of NBS scenarios (porous pavement, rain garden, green roof, and combined) are quantified with the help of their fractal dimension. We point out the consequences of their estimates. Then, a fully distributed and physically based hydrological model (Multi-Hydro) was applied to consider the studied catchment and these NBS scenarios with a spatial resolution of 10 m. A total of two approaches for processing the rainfall data were considered for three rainfall events, namely gridded and catchment averaged. These simulations show that the impact of the spatial variability in rainfall on the uncertainty of peak flow of NBS scenarios ranges from about 8 % to 18 %, which is more significant than those of the total runoff volume. In addition, the spatial variability in the rainfall intensity at the largest rainfall peak responds almost linearly to the uncertainty of the peak flow of NBS scenarios. However, the hydrological responses of NBS scenarios are less affected by the spatial distribution of NBSs. Finally, the intersection of the spatial variability in rainfall and the spatial arrangement of NBSs produces a somewhat significant effect on the peak flow of green roof scenarios and the total runoff volume of combined scenarios.

Space variability of hydrological responses of Nature-Based Solutions and the resulting uncertainty

During the last decades, the urban hydrological cycle has been strongly modified by the built environment, resulting in fast runoff and increasing the risk of waterlogging. Nature-Based Solutions (NBS), which apply green infrastructures, have been more and more widely considered as a sustainable approach for urban stormwater management. However, the assessment of NBS performance still requires further modelling development because of their hydrological responses sensitively depends on the representation of multiscale space variability of both the rainfall and the NBS distribution. Indeed, we initially argue this issue with the help of the multifractal intersection theorem. To illustrate the importance of this question, the spatial heterogeneous distributions of two series of NBS scenarios (porous pavement, rain garden, green roof, and combined) are quantified with the help of their fractal dimension. We point out consequences of their estimates. Then, a fully-distributed and physically-based hydrological model (Multi-Hydro) was applied to consider the studied catchment and these NBS scenarios with a spatial resolution of 10 m under two different types of rainfall: distributed and uniform, and for three rainfall events. These simulations show that the impact of spatial variability of rainfall on the uncertainty of peak flow of NBS scenarios ranges from about 8 % to 17 %, which is more pronounced than those of the total runoff volume. In addition, the spatial variability of the rainfall intensity at the largest rainfall peak responds almost linearly to the uncertainty of the peak flow of NBS scenarios. However, the hydrological responses of NBS scenarios are less affected by the spatial distribution of NBS. Finally, the intersection effects of the spatial variability of rainfall and the spatial arrangement of NBS seem more pronounced for the peak flow of green roof scenarios and the total runoff volume of combined scenarios.

Little dimension and the improved new intersection theorem

Let $R$ be a commutative noetherian local ring. We define a new invariant for $R$-modules which we call the little dimension. Using it, we extend the improved new intersection theorem.